# 10.E: Nuclear and Chemical Reactions (Exercises)

These are homework exercises to accompany Chapter 10 of the University of Kentucky's LibreText for CHE 103 - Chemistry for Allied Health. Answers are below the questions.

## Questions

Q10.1.1

Write the symbol for the isotope described.

1. 12 protons, 12 electrons, 13 neutrons
2. 17 protons, 17 electrons, 20 neutrons
3. 53 protons, 53 electrons, 78 neutrons
4. 92 protons, 92 electrons, 146 neutrons

Q10.1.2

Determine the number of protons, neutrons, and electrons in each isotope.

1. $$\ce{^{195}_{77}Ir}$$
2. $$\ce{^{209}_{82}Pb}$$
3. $$\ce{^{211}_{84}Po}$$
4. $$\ce{^{237}_{93}Np}$$

Q10.1.3

Fill in the missing numbers in each equation.

1. $$\ce{^{196}_{82}Pb}$$ + $$\ce{^0_{-1}e}$$ → $$_{\text{__}}^{\text{__}}\text{Tl}$$
2. $$\ce{^{28}_{15}P}$$ → $$_{\text{__}}^{\text{__}}\text{Si}$$ + $$\ce{^0_1e}$$
3. $$\ce{^{226}_{88}Ra}$$ → $$_{\text{__}}^{\text{__}}\text{Rn}$$ + $$\ce{^4_2 \alpha}$$
4. $$\ce{^{73}_{30}Zn}$$ → $$_{\text{__}}^{\text{__}}\text{Ga}$$ + $$\ce{^0_{-1}e}$$

Q10.1.4

Fill in the blanks for each of the nuclear reactions below. State the type of decay in each case.

1. $$\ce{^{198}_{79}Au}$$ → _______ + $$\ce{^0_{-1}e}$$
2. $$ce{^{57}_{27}Co}$$ + $$\ce{^0_{-1}e}$$ → _______
3. $$\ce{^{230}_{92}U}$$ → _______ + $$\ce{^4_2He}$$
4. $$\ce{^{128}_{56}Ba}$$ → _______ + $$\ce{^0_{1}e}$$
5. $$\ce{^{131}_{53}I}$$ → $$\ce{^{131}_{54}Xe}$$ + _______
6. $$\ce{^{239}_{94}Pu}$$ → $$\ce{^{235}_{92}U}$$ + _______

Q10.1.5

Write balanced nuclear reactions for each of the following.

1. Francium-220 undergoes alpha decay.
2. Arsenic-76 undergoes beta decay.
3. Uranium-231 captures an electron.
4. Promethium-143 emits a positron.

### 10.2: Fission and Fusion

Q10.2.1

Describe the main difference between fission and fusion.

Q10.2.2

What is the difference between the fission reactions used in nuclear power plants and nuclear weapons?

Q10.2.3

How do the doses of radioisotopes used in diagnostic procedures and therapeutic treatment compare to one another?

### 10.3: Half-Life

Q10.3.1

What percent of a sample remains after one half-life? Three half-lives?

Q10.3.2

The half-life of polonium-218 is 3.0 min. How much of a 0.540 mg sample would remain after 9.0 minutes have passed?

Q10.3.3

The half-life of hydrogen-3, commonly known as tritium, is 12.26 years. If 4.48 mg of tritium has decayed to 0.280 mg, how much time has passed?

Q10.3.4

The half-life of protactinium-234 is 6.69 hours. If a 0.812 mg sample of Pa-239 decays for 40.14 hours, what mass of the isotope remains?

Q10.3.5

2.86 g of a certain radioisotope decays to 0.358 g over a period of 22.8 minutes. What is the half-life of the radioisotope?

Q10.3.6

Use Table 10.3.2 above to determine the time it takes for 100. mg of carbon-14 to decay to 6.25 mg.

Q10.3.7

A radioisotope decays from 55.9 g to 6.99 g over a period of 72.5 hours. What is the half-life of the isotope?

Q10.3.8

A sample of a radioisotope with a half-life of 9.0 hours has an activity of 25.4 mCi after 36 hours. What was the original activity of the sample?

Q10.3.9

What volume of a radioisotope should be given if a patient needs 125 mCi of a solution which contains 45 mCi in 5.0 mL?

Q10.3.10

Sodium-24 is used to treat leukemia. A 36-kg patient is prescribed 145 μCi/kg and it is supplied to the hospital in a vial containing 250 μCi/mL. What volume should be given to the patient?

Q10.3.11

Using information from the previous question and knowing the half-life of Na-24 is 15 hours, calculate the total dose in μCi given to the patient. How long will it take for the radioactivity to be approximately 80 μCi?

Q10.3.12

Lead-212 is one of the radioisotopes used in the treatment of breast cancer. A patient needs a 15 μCi dose and it is supplied as a solution with a concentration of 2.5 μCi/mL. What volume does the patient need? Given the half-life of lead is 10.6 hours, what will be the radioactivity of the sample after approximately four days?

### 10.4: Physical and Chemical Changes

Q10.4.1

Identify each of the following as a physical or chemical change.

1. melting ice
2. boiling water
3. cooking eggs
4. dissolving salt in water
5. burning match
6. metal reacting with HCl
7. mixing NaCl and KCl
8. decomposition of hydrogen peroxide

Q10.4.2

Give two signs that indicate a chemical change is occurring.

Q10.4.3

What doesn't change when a substance undergoes a physical change?

### 10.5: Chemical Equations

Q10.5.1

Identify the reactants and products in each chemical reaction.

1. In photosynthesis, carbon dioxide and water react to form glucose and oxygen.
2. Magnesium oxide forms when magnesium is exposed to oxygen gas.

Q10.5.2

Write grammatically correct sentences that completely describe the chemical reactions shown in each equation. You may need to look up the names of elements or compounds.

1. 2H2O2(l) → 2H2O(l) + O2(g)
2. CuCO3(s) → CuO(s) + CO2(g)
3. 2Cs(s) + 2H2O(l) → 2CsOH(aq) + H2(g)

Q10.5.3

How many atoms of each element are represented by the following combinations of coefficients and chemical formulas?

1. 5Br2
2. 2NH3
3. 4(NH4)2SO4
4. 2CH3COOH
5. 3Fe(NO3)3
6. 2K3PO4

Q10.5.4

Balance the following equations.

1. Zn(s) + HCl(aq) → ZnCl2(aq) + H2(g)
2. Li(s) + N2(g) → Li3N(s)
3. Ca(OH)2 + HBr → CaBr2 + H2O
4. C4H10 + O2 → CO2 + H2O
5. NH3 + CuO → Cu + N2 + H2O

Q10.5.5

Balance the following equations.

1. Fe(s) + Cl2(g) → FeCl3(g)
2. C4H10O + O2 → CO2 + H2O
3. As + NaOH → Na3AsO3 + H2
4. SiO2 + HF → SiF4 + H2O
5. N2 + O2 + H2O → HNO3

Q10.1.1

Write the symbol for the isotope described.

1. $$_{12}^{25}\text{Mg}$$
2. $$_{17}^{37}\text{Cl}$$
3. $$_{53}^{131}\text{I}$$
4. $$_{92}^{238}\text{U}$$

Q10.1.2

1. 77 protons, 77 electrons, 118 neutrons
2. 82 protons, 82 electrons, 127 neutrons
3. 84 protons, 84 electrons, 127 neutrons
4. 93 protons, 93 electrons, 144 neutrons

Q10.1.3

1. $$\ce{^{196}_{82}Pb}$$ + $$\ce{^0_{-1}e}$$ →$$_{81}^{196}\text{Tl}$$
2. $$\ce{^{28}_{15}P}$$ → $$_{14}^{28}\text{Si}$$ + $$\ce{^0_1e}$$
3. $$\ce{^{226}_{88}Ra}$$ → $$_{86}^{222}\text{Rn}$$ + $$\ce{^4_2 \alpha}$$
4. $$\ce{^{73}_{30}Zn}$$ → $$_{31}^{73}\text{Ga}$$ + $$\ce{^0_{-1}e}$$

Q10.1.4

1. $$\ce{^{198}_{79}Au}$$ → $$_{80}^{198}\text{Hg}$$ + $$\ce{^0_{-1}e}$$, beta
2. $$\ce{^{57}_{27}Co}$$ + $$\ce{^0_{-1}e}$$ → $$_{26}^{57}\text{Fe}$$, electron capture
3. $$\ce{^{230}_{92}U}$$ → $$_{90}^{226}\text{Th}$$ + $$\ce{^4_2He}$$, alpha
4. $$\ce{^{128}_{56}Ba}$$ → $$_{55}^{128}\text{Cs}$$ + $$\ce{^0_{1}e}$$, positron
5. $$\ce{^{131}_{53}I}$$ → $$\ce{^{131}_{54}Xe}$$ + $$_{-1}^{0}e$$, beta
6. $$\ce{^{239}_{94}Pu}$$ → $$\ce{^{235}_{92}U}$$ + $$_{2}^{4}\alpha$$ (or can show as $$_{2}^{4}\text{He}$$), alpha

Q10.1.5

1. $$_{87}^{220}\text{Fr}\;\rightarrow\;_{2}^{4}\text{He}\;+\;_{85}^{216}\text{At}$$
2. $$_{33}^{76}\text{As}\;\rightarrow\;_{-1}^{0}e\;+\;_{34}^{76}\text{Se}$$
3. $$_{92}^{231}\text{U}\;+\;_{-1}^{0}e\;\rightarrow\;_{91}^{231}\text{Pa}$$
4. $$_{61}^{143}\text{Pm}\;\rightarrow\;_{1}^{0}e\;+\;_{60}^{143}\text{Nd}$$

### 10.2: Fission and Fusion

Q10.2.1

During fission, big nuclei split into smaller nuclei. During fusion, nuclei combine to form large nuclei.

Q10.2.2

Fission in nuclear power plants is controlled through limiting the availability of neutrons. Nuclear weapons are uncontrolled once the process initiates.

Q10.2.3

Diagnostic amounts are much smaller than therapeutic amounts.

### 10.3: Half-Life

Q10.3.1

1 half-life: 50%

3 half-lives: 12.5%

Q10.3.2

 Time Half-lives Amount 0 minutes 0.540 mg 3 minutes 1 0.270 mg 6 minutes 2 0.135 mg 9 minutes 3 0.0675 mg

Q10.3.3

 Amount Half-lives Time 4.48 mg 0 years 2.24 mg 1 12.26 years 1.12 mg 2 24.52 years 0.560 mg 3 36.78 years 0.280 mg 4 49.04 years

Q10.3.4

 Time Half-lives Amount 0 hours 0.812 mg 6.69 hours 1 0.406 mg 13.38 hours 2 0.203 mg 20.07 hours 3 0.102 mg 26.76 hours 4 0.0508 mg 33.45 hours 5 0.0254 mg 40.14 hours 6 0.0127 mg

Q10.3.5

 Amount Half-lives 2.86 g 1.43 g 1 0.715 g 2 0.358 g 3

It takes three half-lives to go from 2.86 g to 0.358 g in a total time of 22.8 minutes.

$$22.8\;min\;\div\;3\;=7.60 \;min$$

One half-life is 7.60 minutes.

Q10.3.6

 Amount Half-lives Time 100. mg 0 years 50.0 mg 1 5730 years 25.0 mg 2 11460 years 12.5 mg 3 17190 years 6.25 mg 4 22920 years

Q10.3.7

 Amount Half-lives 55.9 g 28.0 g 1 14.0 g 2 6.99 g 3

It takes three half-lives to go from 55.9 g to 6.99 g in a total time of 72.5 hours.

$$72.5\;hr\;\div\;3\;=24.2 \;hr$$

One half-life is 24.2 hours.

Q10.3.8

Fill in the time and half-lives from top to bottom. Start at the bottom of the amount column to fill it in because we know where we end up but not where we started.

 Time Half-lives Activity 0 hours 406 mCi 9.0 hours 1 203 mCi 18 hours 2 102 mCi 27 hours 3 50.8 mCi 36 hours 4 25.4 mCi $$\leftarrow$$ START HERE

Q10.3.9

$$125\;mCi\left(\frac{5.0\;mL}{45\;mCi}\right)=14\;mL$$

Q10.3.10

Sodium-24 is used to treat leukemia. A 36-kg patient is prescribed 145 μCi/kg and it is supplied to the hospital in a vial containing 250 μCi/mL. What volume should be given to the patient?

$$36\;kg\left(\frac{145\;\mu Ci}{kg}\right)\left(\frac{1\;mL}{250\;\mu Ci}\right)=21\;mL$$

Q10.3.11

$$21\;mL\left(\frac{250\;\mu Ci}{mL}\right)=5250\;\mu Ci$$ is the total dose received

 Amount Half-lives Time 5250 μCi 0 hours 2625 μCi 1 15 hours 1313 μCi 2 30 hours 656 μCi 3 45 hours 328 μCi 4 60 hours 164 μCi 5 75 hours 82 μCi 6 90 hours

Q10.3.12

Lead-212 is one of the radioisotopes used in the treatment of breast cancer. A patient needs a 15 μCi dose and it is supplied as a solution with a concentration of 2.5 μCi/mL. What volume does the patient need? Given the half-life of lead is 10.6 hours, what will be the radioactivity of the sample after approximately four days?

Volume given: $$15\;\mu Ci\left(\frac{1\;mL}{2.5\;\mu Ci}\right)=6.0\;mL$$

Elapsed time in hours: $$4\;days\left(\frac{24\;hr}{day}\right)=96\;hr$$

 Time Half-lives Activity 0 hours 15 μCi 10.6 hours 1 7.5 μCi 21.2 hours 2 3.8 μCi 31.8 hours 3 1.9 μCi 42.4 hours 4 0.94 μCi 53.0 hours 5 0.47 μCi 63.6. hours 6 0.23 μCi 74.2 hours 7 0.12 μCi 84.8 hours 8 0.059 μCi 95.6 hours 9 0.029 μCi

### 10.4: Physical and Chemical Changes

Q10.4.1

1. physical
2. physical
3. chemical
4. physical
5. chemical
6. chemical
7. physical
8. chemical

Q10.4.2

Any two from change in color, formation of gas (i.e. bubbles), formation of precipitate, odor, change in temperature.

Q10.4.3

chemical composition (i.e. chemical formula is the same)

### 10.5: Chemical Equations

Q10.5.1

1. reactants: carbon dioxide and water; products: glucose and oxygen
2. reactants: magnesium and oxygen; product: magnesium oxide

Q10.5.2

Descriptions may vary.

1. Two moles of liquid hydrogen peroxide decomposes to form two moles of liquid water and one mole of gaseous hydrogen.
2. One mole of solid copper(II) carbonate decomposes to form one mole each of solid copper(II) oxide and gaseous carbon dioxide.
3. Two moles of solid cesium react with 2 moles of liquid water to form 2 moles of aqueous cesium hydroxide and 1 mole of gaseous hydrogen.

Q10.5.3

1. 10 Br
2. 2 N, 6 H
3. 8 N, 32 H, 4 S, 16 O
4. 4 C, 8 H, 4 O
5. 3 Fe, 9 N, 27 O
6. 6 K, 2 P, 8 O

Q10.5.4

1. Zn(s) + 2 HCl(aq) → ZnCl2(aq) + H2(g)
2. 6 Li(s) + N2(g) → 2 Li3N(s)
3. Ca(OH)2 + 2 HBr → CaBr2 + 2 H2O
4. 2 C4H10 + 13 O28 CO2 + 10 H2O
5. 2 NH3 + 3 CuO → 3 Cu + N2 + 3 H2O

Q10.5.5

1. 2 Fe(s) + 3 Cl2(g) → 2 FeCl3(g)
2. C4H10O + 6 O24 CO2 + 5 H2O
3. 2 As + 6 NaOH → 2 Na3AsO3 + 3 H2
4. SiO2 + 4 HF → SiF4 + 2 H2O
5. 2 N2 + 5 O2 + 2 H2O → 4 HNO3